In mathematics, a degenerate case is a limiting case in which a class of object changes its nature so as to belong to another, usually simpler, class. Wikibooks Wikiversity has more about this subject: School of Mathematics Wikiquote has a collection of quotations related to: Mathematics Look up Mathematics on Wiktionary, the free dictionary Wikimedia Commons has more media related to: Mathematics Bogomolny, Alexander: Interactive Mathematics Miscellany and Puzzles. ...

• A point is a degenerate case of a circle, namely one with radius 0. The circle is a degenerate form of an ellipse, namely one with eccentricity 0.
• The line is a degenerate form of a parabola if the parabola resides on a tangent plane.
• A hyperbola can degenerate into two lines crossing at a point, through a family of hyperbolas having those lines as common asymptotes.
• See "general position" for other examples.

Another usage of the word comes in eigenproblems: a degenerate eigenvalue is one that has more than one linearly independent eigenvector. Jump to: navigation, search The word point can refer to: Look up Point on Wiktionary, the free dictionary a location in physical space a unit of angular measurement; see navigation the point that is a typographic unit of measure equal inch or sometimes approximated as inch; on computer displays it... Jump to: navigation, search In Euclidean geometry, a circle is the set of all points at a fixed distance, called the radius, from a fixed point, called the centre (center). ... In mathematics, an ellipse (from the Greek for absence) is a plane algebraic curve where the sum of the distances from any point on the curve to two fixed points is constant. ... (This page refers to eccitricity in mathematics. ... A line, or straight line, is, roughly speaking, an (infinitely) thin, (infinitely) long, straight geometrical object, i. ... A parabola The parabola (from the Greek: παραβολή) is a conic section generated by the intersection of a cone and a plane tangent to the cone or parallel to some plane tangent to the cone. ... In differential geometry, one can attach to every point p of a differentiable manifold a tangent space, a real vector space which intuitively contains the possible directions in which one can pass through p. ... A graph of a hyperbola, where h = k = 0 and a = b = 2. ... An asymptote is a straight line which accompanies a curve at an arbitrary distance. ... In geometry, general position for a set of points, or other configuration, means the general case situation, as opposed to some more special or coincidental cases that are possible. ... In mathematics, a number is called an eigenvalue of a matrix if there exists a nonzero vector such that the matrix times the vector is equal to the same vector multiplied by the eigenvalue. ... In linear algebra, the eigenvectors (from the German eigen meaning own) of a linear operator are non-zero vectors which, when operated on by the operator, result in a scalar multiple of themselves. ...

See also: degeneracy, Trivial (mathematics). The word degeneracy has more than one meaning: In general, degeneracy means reverting to an earlier, simpler, state In mathematics, a limiting case in which a class of object changes its nature so as to belong to another, usually simpler, class. ... Jump to: navigation, search In mathematics, the term trivial is frequently used for objects (for examples, groups or topological spaces) that have a very simple structure. ...